DrunkWalk: Collaborative and Adaptive Planning for Navigation of Micro-Aerial Sensor Swarms

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1 DrunkWalk: Collaboraive and Adapive Planning for Navigaion of Micro-Aerial Sensor Swarms Xinlei Chen Carnegie Mellon Universiy Pisburgh, PA, USA Aveek Purohi Carnegie Mellon Universiy Pisburgh, PA, USA Carlos Ruiz Dominguez Carnegie Mellon Universiy Pisburgh, PA, USA Sefano Carpin UC Merced Merced, CA, USA Pei Zhang Carnegie Mellon Universiy Pisburgh, PA, USA ABSTRACT Micro-aerial vehicle (MAV) swarms are a new class of mobile sensor neworks wih many applicaions, including search and rescue, urban surveillance, radiaion monioring, ec. These sensing applicaions require auonomously navigaing a high number of low-cos, low-complexiy MAV sensor nodes in hazardous environmens. The lack of preexising localizaion infrasrucure and he limied sensing, compuing, and communicaion abiliies of individual nodes makes i challenging for nodes o auonomously navigae o suiable preassigned locaions. In his paper, we presen a collaboraive and adapive algorihm for resource-consrained MAV nodes o quickly and efficienly navigae o preassigned locaions. Using radio fingerprins beween flying and landed MAVs acing as radio beacons, he algorihm deecs inersecions in rajecories of mobile nodes. The algorihm combines noisy dead-reckoning measuremens from muliple MAVs a deeced inersecions o improve he accuracy of he MAVs locaion esimaions. In addiion, he algorihm plans inersecing rajecories of MAV nodes o aid he locaion esimaion and provide desired performance in erms of imeliness and accuracy of navigaion. We evaluae he performance of our algorihm hrough a real esbed implemenaion and large-scale physical feaure based simulaions. Our resuls show ha, compared o exising auonomous navigaion sraegies, our algorihm achieves up o 6 reducion in locaion esimaion errors, and as much as 3 improvemen in navigaion success rae under he given ime and accuracy consrains. Caegories and Subjec Descripors Permission o make digial or hard copies of all or par of his work for personal or classroom use is graned wihou fee provided ha copies are no made or disribued for profi or commercial advanage and ha copies bear his noice and he full ciaion on he firs page. Copyrighs for componens of his work owned by ohers han ACM mus be honored. Absracing wih credi is permied. To copy oherwise, or republish, o pos on servers or o redisribue o liss, requires prior specific permission and/or a fee. Reques permissions from Permissions@acm.org. SenSys 15, November 1 4, 2015, Seoul, Souh Korea.. c 2015 ACM. ISBN /15/11...$ DOI: hp://dx.doi.org/ / C.2 [Compuer-Communicaion Neworks]: Disribued Sysems Disribued applicaions; I.2 [Arificial Inelligence]: Disribued Arificial Inelligence Muliagen sysems Keywords Mobile Sensor Neworks, Micro-Aerial Vehicle, Swarm 1. INTRODUCTION Many hosile, dangerous, or oherwise inaccessible environmens (such as urban search and rescue, environmenal monioring, surveillance, ec.), siuaional awareness is needed. However, in hese dangerous scenarios, manual deploymen of sensors is ofen no feasible. In such scenarios, auonomously navigaing MAV swarms o a se of goal locaions, in accordance wih he needs of domain expers, can provide significan benefi. Furher, uilizing a large number of low-cos, low-complexiy mobile sensor nodes, as opposed o using a limied number of sophisicaed robos, can be more cos effecive and provide increased robusness hrough redundancy. In addiion, small lighweigh mobile sensor nodes provide greaer safey as he effecs of heir collisions wih he objecs or persons in he indoor environmen are inconsequenial. MAV swarms are an emerging class of neworked mobile sysems wih widespread applicaions in such domains. These swarms consis of miniaure aerial sensor nodes wih limied individual sensing, compuing and communicaion capabiliies [1, 2]. Iniial work in he operaion of MAVs has focused on oudoor or highly insrumened environmens ha rely on exernal sensors o conrol individual devices [3, 4]. However, such cenralized sensing approaches are hampered in indoor environmens by obsrucions (walls, furniure, ec.). A he same ime, reliance on sensing infrasrucure implies requiremen for a large deploymen of suppor sensors covering all he locaions ha a MAV may visi [5]. Thus hese approaches are only applicable in pre-surveyed locaions.

2 This paper presens DrunkWalk, a echnique for cooperaive and adapive navigaion of swarms of micro-aerial sensors in environmens no formerly precondiioned for operaion. The key focus behind his neworked MAV swarm research is o rely on collaboraion o overcome limiaions of individual nodes and efficienly achieve sysem-wide sensing objecives. In DrunkWalk, he MAV swarm self-esablishes a emporary infrasrucure of a few landed MAV s acing as radio beacons. Using radio signaure or fingerprins from beacon nodes, he algorihm deecs inersecions in rajecories of exploring mobile MAV nodes. The algorihm combines noisy dead-reckoning measuremens from muliple MAVs a he deeced inersecions o improve he accuracy of he MAVs locaion esimaes. Mos imporanly, he algorihm adapively plans rajecories of MAV nodes according o he cerainy of heir locaion esimaions direcing movemen o improve locaion esimaes when cerainy is low, and direcing MAV o he goal locaion when cerainy of locaion esimaes is high. The adapive sraegy enables DrunkWalk o improve he locaion esimaion accuracy and success rae of navigaion under given ime and accuracy consrains. The main conribuions of his paper are: An adapive planning algorihm for navigaion ha enables he swarm o collaboraively achieve up o 6 reducion in locaion esimaion errors, and as much as 3 improvemen in navigaion success rae under he given ime and accuracy consrains. A planning algorihm ha deermines he qualiy of locaion esimaions and uses i o adapively plan node moion. Real MAV esbed experimens and large scale physical feaure based simulaions using radio signaures colleced from he physical world and empirically deermined sensor noise models validaing our assumpions. The res of his paper is organized as follows. Secion 2 gives a high level overview of he archiecure and operaion of he sysem. Secion 3 gives a deailed echnical descripion of he various algorihms presened in he paper. Secion 4 evaluaes and analyzes he sysem hrough exensive simulaions and validaes assumpions hrough MAV esbed experimens. Furher discussion of some exra sysem deails are saed in Secion 5. In Secion 6, we describe relaed work and discuss he sae-of-he-ar infrasrucure-free navigaion echniques in conex of MAV swarm deploymen. Finally, we draw conclusions and summarize our conribuions in Secion OVERVIEW Poenial MAV swarm sensing applicaions will require mobile sensors o auonomously navigae o desired locaions in operaing environmens wih no localizaion infrasrucure. In his paper, we address he problem of how a nework of mobile sensors can be navigaed o pre-deermined posiions under ime and accuracy consrains. 2.1 Operaion & Archiecure The sysem begins operaion wih a swarm of MAV s being inroduced ino he operaing environmens. We make he Figure 1: The figure shows he archiecure of our navigaion sysem. The mobile MAV nodes send dead-reckoning sensor daa and radio signaures o a base saion. The base runs he DrunkWalk esimaion and planning algorihm and issues movemen commands o individual MAV nodes. assumpion ha a coarse map of he building is available and can be uilized by domain expers o pre-deermine suiable placemen of sensors. This is a valid assumpion in mos scenarios, as emergency response personnel have access o he rough floor-plans of buildings hrough ciy regisries, and hanks o increased availabiliy of indoor maps ailored o locaion based services (e.g., indoor Google maps). The proposed sysem has 3 major operaional phases: seup, esimaion and planning (he laer wo proceed in conjuncion): Seup: The sysem auonomously esablishes a ransien infrasrucure of saionary MAV nodes acing as wireless beacons. These nodes land upon being inroduced ino he area and remain saionary during he process. The objecive of he saionary nodes is o enable mobile MAV nodes o obain radio signaures or fingerprins of locaions raversed on heir pahs. These nodes use a simple dispersion algorihm [6, 7] ha les hem spread ou in he environmen wihou any esimaion of heir locaion. Esimaion: The sysem hen desires o esimae he locaions of nodes in order o guide hem o heir goal locaions. To realize his, he sysem firs uses dead reckoning sensors such as an opical flow velociy sensor and magneomeer (in our es MAV plaform) o ge a rough esimae of he moion pah of mobile nodes. Second, he sysem uses radio fingerprins, colleced by mobile nodes from he self-esablished wireless beacons, o deermine snapsho poins, i.e. locaion poins ha were previously visied by oher nodes or by iself. Finally, he sysem uses he snapsho poins o combine locaion esimaes from muliple nodes and collaboraively improve locaion esimaions of he enire swarm. Planning: Having esimaed locaions, he sysem plans pahs for each node ha 1) leads o subsequen goal posiions and 2) improves locaion esimaion accuracy. The qualiy of he planned pah depends grealy on he accuracy of he iniial locaion esimae of nodes. A bad locaion esimae will render any aemp o plan a deerminisic pah useless when he nodes don know where hey are, hey canno plan a correc pah o heir desinaion.

3 Our sysem hus considers he qualiy of locaion esimaion in planning node pahs. The pah planner commands nodes movemen such ha hey increase he number of snapsho poins and poenially improve locaion esimaes when he qualiy of heir esimaes is likely o be low. On he oher hand, when he locaion esimaes are likely o be more accurae, he planner uses he map o direc hem o heir designaed goal locaions. Figure 1 shows he archiecure of he sysem. Through dispersion algorihm, he sysem deploys Saionary MAV Nodes ha ac as wireless beacons. Mobile MAV Nodes explore and obain dead-reckoning measuremens from heir on-board sensors and radio RF-signaures from he saionary beacons. The mobile nodes relay his o a Base. The Base sores a daabase of known radio signaures (Signaure DB) ha is used o deermine snapsho poin in node pahs and apply correcions o heir dead-reckoning esimaes. The correced locaion esimaes are used by he Base in conjuncion wih a coarse map (indoor layou wih locaion of walls and doors) of he environmen o command he subsequen movemens of MAV nodes. 2.2 Improving Locaion Esimaion Through Swarms The core idea behind our esimaion approach is o use relaively large number of mobile sensors in he swarm o collaboraively reduce he error. This is achieved by deecing when nodes move over he same space in he environmen and combining heir individual locaion esimaions a hese poins. Errors in dead reckoning measuremens are mainly due o noise in inerial sensors ha are independen across nodes and ime [8]. Thus, combining esimaes from muliple nodes and propagaing correcions o hem improves heir locaion esimaions. Figure 2 illusraes he on-line process of deermining snapsho poin from radio measuremens Deermining Snapsho Poins The locaion esimaion requires a node o be able o deermine when i visis a locaion previously visied by iself or by anoher nodes - a snapsho. The snapsho poin provides he opporuniy o combine esimaions from muliple independen mobile nodes and improve locaion esimaions. The sysem deermines a snapsho poin using radio fingerprins colleced by mobile nodes from he self-esablished beacon nodes. The radio fingerprins are colleced in an online fashion, i.e., he nodes discover fingerprins as hey explore he space. These fingerprins are sen o he Base and mached wih a daabase of previously discovered signaures. If he signaure maches an exising signaure in he daabase (decided by a cosine disance and a hreshold), he poin is classified as a snapsho poin and a correcion can be applied o he curren locaion esimaion. If he signaure does no mach any exising signaures, i is added o he daabase as a new enry Combining Esimaes a Snapsho Poins The process of combining locaion esimaions mus be performed carefully. The naive approach would be o ake he average of all locaion esimaes for a paricular snapsho Figure 2: The figure shows he process of deermining snapsho poins. (a) Node 1 moves and obains a radio signaure from saionary MAV. This is enered ino he he Base Signaure DB as new signaure. (b) When Node 2 visis he same locaion, is colleced radio signaure maches exising signaure and a correcion can be performed a he Base. poin. However, his approach does no consider he naure of he underlying disribuion of noise in locaion esimaions ha ofen does no follow a normal disribuion especially in indoor environmens. Combining esimaions is a chicken and egg problem ha requires a snapsho poin o esimae and updae is own locaion from visiing mobile nodes, and subsequenly, use he updaed locaion o correc he esimaes of he visiing mobile nodes. To achieve his, we employ a paricle filer based approach. A paricle filer [9] is a Bayesian esimaion mehod o esimae sysem sae based on muliple noisy sensor measuremens. We use a paricle filer o rack he posiion and orienaion of each mobile node. Similarly, we use a paricle filer o rack he posiion of each snapsho poin as i is discovered and visied by he MAV nodes. Every visi o a snapsho poin by a mobile node resuls in he he mobile node correcing he esimaion of he paricles of he snapsho poin, which in urn correcs he esimaions of he paricles of he mobile node. The various esimaion algorihms are described in deail in Secion Adapive Pah Planning We described how a snapsho poin beween he pahs of nodes can be uilized o improve locaion esimaes. Planning pahs is hus he second chicken and egg problem encounered in navigaion. Beer locaion esimaes are needed by nodes o navigae o predeermined regions quickly. However, a he same ime, achieving beer locaion esimaions may require nodes o ake deours (o find snapsho poins) cosing ime and energy. The planning componen of our sysem seeks o make a suiable rade-off beween hese aspecs of navigaion DrunkWalk In order o reach he goal regions, we use an indoor layou wih locaion of walls and doors of he environmen. I

4 should be noed ha he algorihm does no require high qualiy maps wih informaion of he posiion of obsacles. Such rough maps are generally available or easy o obain in mos applicaion scenarios. The rough map enables us o bias he direcion of node movemen owards predeermined goal regions, if he curren locaion of he node in he map can be reasonably deermined. However, due o noisy sensors, he locaion of individual nodes canno always be esimaed correcly, which makes i difficul o consisenly plan correc pahs. The sysem aemps o solve his by operaing in wo modes: Exploraion: In his mode, he MAV node aemps o seek snapsho poins ha can poenially improve he locaion esimaes of he MAV node. This is execued when he qualiy of locaion esimaions (deermined by he enropy of he racking paricle filer disribuion) is low. Navigaion: In his mode, he MAV node aemps o follow he direcion of he bias from he graph using he esimaed locaion from he DrunkWalk algorihm. This is execued when he qualiy of locaion esimaes is high. I is easy o see ha he performance of he navigaion sep depends on he oucome of exploraion sep. However, he exploraion sep requires exra use of resources ha increases he ime of navigaion. Therefore, he Drunk- Walk algorihm seeks o opimize his rade-off by adapively swiching beween hese wo modes. 3. DESCRIPTION This secion provides a deailed descripion of he major componens of our proposed sysem. Firs, his secion describes how he locaion and orienaion of he MAVs and he posiions of he signaures are esimaed over ime using a se of paricle filers. A separae paricle filer is associaed o each MAV in he eam and each RF-signaure being localized in space. Therefore, paricles esimaing he posiion and orienaion of he MAVs include he componens c x, c y, c φ, whereas paricles esimaing he locaion of he signaures include componens s x, s y for he posiion. As described in Secion 2, a base saion exchanges informaion wih he MAVs (commands and measuremens) and mainains a daabase of known signaures (see Figure 1). Due o he limied on-board compuaional power on he MAV, our curren implemenaion performs all compuaions in he base. 3.1 Paricle Filer Background A paricle filer is a Bayesian esimaion mehod using a finie number of elemens (so called paricles) o represen a non-parameric probabiliy densiy. I was inroduced in he fifies [10] and became popular in roboics in he las wo decades [9]. As a specific implemenaion of a more general recursive Bayes filer under he Markov assumpion, i requires assumpion of availabiliy of wo probabilisic models, namely he sae evoluion model (ofen called moion model in mobile or roboic applicaions) and he measuremen model. Assuming he unknown sae o be esimaed a ime is indicaed by x, he sae evoluion model provides p(x x 1, u ) (1) where u is he known command given o he sysem a ime. The measuremen model, insead, is given by p(z x ) (2) where z is he measuremen a ime. Due o he Markov assumpion, x is condiionally independen from x k wih k < 1 once x 1 is known. Similarly, given x, he measuremen z is condiionally independen from any oher variable. Noe ha one does no need o commi o specific disribuions in Eq. 1 and Eq. 2, e.g., hey do no have o be Gaussian disribuions. The generic algorihm o propagae a poserior using a paricle filer is given in Algorihm 1, where we mosly follow he noaion presened in [9]. The algorihm sars wih a se of M paricles X esimaing he poserior of x 1, i.e., he sae x a ime 1. Given he laes command u and measuremen z, i produces a new se of M paricles providing an updaed poserior esimae for x a ime. The ih paricle in X, x [i], represens he ih possible hypohesis abou he sae a ime. Algorihm 1 shows he generic paricle filer algorihm. The firs for loop creaes a new se of M paricles sampling he moion model from he se of exising paricles, while he second for loop implemens he so-called imporance resampling. The se of paricles provides a discree approximaion for he poserior. Daa: X 1, u, z Resul: X 1 X ; 2 X ; 3 for i 1 o M do 4 x [i] 5 w [i] sample p(x x [i] 1, u); p(z x [i] ); 6 X X {< x [i], w [i] >}; 7 end 8 for i 1 o M do 9 draw j wih probabiliy α w [j] ; 10 X X {x [j] }; 11 end Algorihm 1: Generic paricle filer algorihm 3.2 MAV Locaion Tracking In his subsecion, we show how he generic paricle filer esimaor can be specialized o esimae he locaion of he MAVs. To reduce he compuaional complexiy, raher han implemening a cenralized paricle filer joinly esimaing he locaion of all he MAVs, we associae a paricle filer o each MAV. Assuming here are N M MAVs involved in he navigaion ask, he sysem hen creaes and updaes N M paricle filers. Each filer is iniialized wih M = 100 paricles uniformly disribued in he area. All compuaions ake place on he base saion Predicion from Moion Models For he predicion sep, i is necessary o use a generaive law o implemen he paricle creaion in line 4 of Algorihm 1. To his end, we use equaions similar o he ones given in [7]. Le he command a ime be u = (v, ω ), where v is

5 he ranslaional velociy and ω is he roaional velociy. Noe ha he conrol sysem always generaes commands in which only one of he wo componens is differen from 0, i.e., he MAV eiher ranslaes or roaes, bu does no make boh movemens a he same ime. Then, a new paricle is generaed as cx c y c φ [i] = cx c y c φ [i] 1 [i] 1 ) 1 ) ω + δ v cos(c φ [i] v sin(c φ (3) where δ is he ime inerval beween wo commands. The correcness of he equaion follows form he assumpion ha only one of v and ω can be differen from 0. Noise is added o he ranslaional and roaional velociies as per he empirically obained acuaion noise models p(n v) and p(n ω) from our es MAV plaform, bu can be specified as per he specific sensor or MAV plaform used. and ω [i] are obained as: v [i] ω [i] = v + n [i] v = ω + n [i] ω Thus, v [i], n [i] v is drawn from p(n v) (4), n [i] ω is drawn from p(n ω) (5) where v and ω are he nominal commands. In our simulaions, according o [7], p(n v) and p(n ω) are specified as normal disribuions wih µ = 0 and σ is expressed as a percenage of he value of v or ω Correcion from Measuremens The correcion sep hinges on he weighs assigned o he paricles (line 5 in Algorihm 1). Each MAV is equipped wih a magneomeer sensor reurning a measuremen for is heading. Moreover, RF-signaure snapsho provides anoher measuremen. These wo measuremens are asynchronous in he sense ha, while he on-board heading sensor can be queried afer each command is execued, signaure maching occurs only when revisiing a locaion associaed wih a known signaure. In he following, we herefore separaely describe, how he wo differen weighs are compued, given ha hey are generaed and used (via resampling) in separae sages. The heading measuremen is sraighforward o inegrae. According o former experimenal measures [11], he nominal heading reurned by he sensor is affeced by Gaussian noise wih a known variance σ 2 (σ = 40 degrees o be precise). Therefore, for he heading weigh we se p(z x ) = f N,σ 2(z c φ [i] ) (6) where f N,σ 2 is he densiy probabiliy of a Gaussian wih 0 mean and variance σ 2 [i], and he argumen z c φ is normalized o accoun for he 2π period. The process is subsanially differen for RF-signaure snapsho poins. In his case, raher han compuing p(z x ), we deermine w [i] hrough a wo seps process. 1) When a signaure is measured, he firs sep is o communicae wih he known signaures daabase o deermine wheher he signaure is new or has been encounered already (eiher by he same MAVs or a differen one). If he daabase deermines he signaure is new, he MAV does no perform he second sep and does no compue weighs (however, he signaure is sored in he daabase and a new paricle filer is creaed; see secion 3.3 for deails.) 2) On he conrary, if he daabase deermines ha a signaure snapsho poins is aking place, he second sep sars. Firs, on he daabase side, he paricle filer esimaing he posiion of he signaure being revisied is updaed (see secion 3.3 for deails.) Afer he RF-signaure paricle filer has been updaed, each paricle in he MAV paricle filer is assigned a weigh as follows. A GMM is creaed saring from he paricles in he signaure being mached. Such GMM is a bidimensional probabiliy densiy funcion wih he following equaion: f GMM (x, y) = 1 M M fn i,σ(x, y) (7) where fn i,σ is a bidimensional Gaussian disribuion wih mean µ = [s [i] x s [i] y ] T and covariance marix Σ (a diagonal marix wih value 2 on he main diagonal). Then, each paricle is assigned he weigh w [i] i=1 f GMM (c x [i] [i], c y ). (8) Afer all weighs have been compued, resampling can ake place as described in Algorihm Adding Paricles Using Coarse Map Due o he unavoidable errors in he esimaion process, we implemened an addiional sep o couner he formerly menioned paricle depleion problem. Afer he new se X has been creaed, we deermine he locaion wih he highes number of paricles. Le v d be his locaion, and le N be he se of neighbor nodes according o he coarse map. Then, he 25 paricles wih he lowes weigh are discarded and replaced by an equal number of paricles generaed using a random disribuion over he space associaed wih he nodes in N. The raionale behind his sep is o generae paricles o recover errors due o he erroneous deerminaion ha a ransiion from a room o he nex effecively ook place. 3.3 Paricle Filer for Snapsho Poins We now describe how he spaial locaion of he signaures can be esimaed using a se of paricle filers. For he MAVs case, we do no compue a cenralized esimaion, bu we raher associae a filer wih each signaure o be racked. This esimaion process has wo main differences wih he posiion and orienaion esimaion for he MAVs. Firs, he number of signaure locaions o be esimaed is no known upfron. So new filers need o be creaed on-he-fly when a new signaure o be localized is idenified. Second, signaures do no move. Therefore he esimaion process does no include a predicion sep, only a correcion sep. As for he MAVs, each filer includes 100 paricles Iniializaion from MAV Paricles As described in he previous subsecion, a new signaure is generaed when he known signaures daabase receives a query from one of he MAVs wih an RF-signaure ha

6 canno be mached o any of he formerly discovered ones. In his case, a new enry in he daabase is creaed and a new paricles filer is insaniaed. The iniial se of paricles for his new filer is copied from he paricles of he vehicle ha discovered he feaure, while discarding he componen relaed o heading because i is irrelevan for he signaure esimaion process Correcion from MAV Paricle Filer Correcion happens when a MAV queries signaure daabase wih a signaure ha can be mached wih one of he enries already discovered. In his case, Algorihm 1 is execued for he signaure filer, wih he excepion of line 4, because no predicion akes place. The weigh for w [i] for he ih paricle is compued as follows. Firs, he posiion of he MAV ha generaed he snapsho poin is deermined by aking he average of is paricles. Noe ha his average is implicily weighed, because hrough he resampling process, paricles wih higher weigh will be included more ofen in he paricle se (see line 9 in Algorihm 1). As a resul, hey will be couned muliple imes when compuing he average. Le x be he compued average posiion of he MAV generaing he mach, and le s [i] 1 be he posiion of he ih paricle in he signaure paricle filer a ime 1, and le d i = x s [i] be he Euclidean disance beween 2 1 he expeced posiion of he MAV and he paricle. weigh of each paricle a ime is hen defined as The w [i] = F d,δ (d + K) F d,δ (d K) (9) where F d,δ is he cumulaive densiy funcion of a Gaussian disribuion wih mean d and variance δ. This formula is based on our experimenal esbed showing ha revisis are correcly deeced when he displacemen beween he original and he new posiion is wihin K meers. The specific values for δ and K depend on he number of anchors and are furher described in Secion Once weighs have been compued, correcion for he esimae of he signaure paricle filer can hen ake place hrough resampling, as described in Algorihm Daabase of Fingerprins In order o help locaion esimaion correcion wih snapsho poins afer each movemen, he sysem mainains a daabase of fingerprins. A fingerprin a a specific locaion is a se of RSSI values from differen saionary nodes measured by he MAV and sored in a dicionary daa srucure. When he node arrives a a new locaion, i calculaes he cosine similariy beween he newly discovered fingerprin and he fingerprins sored in he daabase. A pre-defined hreshold T sig is used o decide wheher i is a new or known fingerprin. 3.4 DrunkWalk Planning In his secion, we describe how he sysem plans he pahs of MAV nodes wih locaion esimaes of varying qualiy in order o deploy quickly. Figure 3 shows a flowchar of he planning algorihm Coarse Map The sysem uses he layou wih locaion of walls and doors of he environmen o exrac a coarse map. The doors are Figure 3: The figure shows he flowchar of he DrunkWalk planning algorihm. The planner adapively changes beween random walk and graph biased movemen based on he enropy of paricle filers racking respecive MAV nodes. usually seleced as he desinaion where we navigae he MAVs. The coarse map makes very few assumpions abou he qualiy of he map bu provides a way o bias he moion of MAV nodes owards designaed locaions Enropy as Qualiy of Locaion Esimaes The enropy of a random variable x can be defined as he expeced informaion ha he value of x carries. In he discree case, i is given by H(x) = E[ log 2 p(x)] (10) which represens he number of bis required o encode using an opimal encoding, assuming ha p(x) is he probabiliy of observing x. The enropy can herefore be used as an indicaion of he uncerainy of he esimae of a paricle filer. The lower he enropy he beer he cerainy of he locaion esimae is, and vice versa. For he paricle filer, we calculae he enropy [9] of he weighs a ime as M H = w [i] log 2 w [i]. (11) i= Exploraion When he enropy of he paricle filer is high (> hreshold T H), he sysem seeks o primarily improve he locaion esimaes. The inuiion here is ha wih an incorrec esimaion of curren locaion, using he bias from he graph is likely o be incorrec. This also resuls in cases where he

7 Figure 4: The figure shows he floor plan of 6 rooms wih a hallway used for physical feaure based simulaion and real esbed experimens. The MAVs sar from he enrance of he building and are navigaed o differen goal areas. MAV may ge suck and can poenially perform worse han a purely random deploymen sraegy. Wih his in mind, he planner employs a random walk sraegy o direc he moion of MAV nodes. Wih random walk, he likelihood of nodes discovering snapsho poins increases and so does he likelihood of improving heir locaion esimaes. This is referred o as he exploraion sep Navigaion Correspondingly, when he uncerainy of locaion esimaes is low (H < T H), he planner commands he nodes o follow he bias indicaed by he coarse map. Wih a more accurae locaion, likelihood of nodes following he bias and hen reaching he inended desinaion increases. A key poin in choosing he direcional bias from he graph is ha i is sampled based on he disribuion of paricles in he node s paricle filer. For example, consider a node wih 20 paricles indicaing is posiion as room 1 and herefore requiring he node o go norh-wes o exi he room, while 80 paricles indicae he node is in room 2 and mus move souh. In his case, he planner samples he movemen direcion according o he disribuion of paricles over he nodes of he graph, i.e., he node has a 20% chance of being commanded o move norh-wes and a 80% chance of receiving a souh command Collision Recovery Sraegy MAV plaforms have very limied sensing capabiliy and ofen do no employ sophisicaed obsacle deecion sensors. Proposed MAV plaforms [1] rely on heir low weigh and ofen use collisions hemselves o discover obsacles. However, a sraegy is needed in dealing wih collision so as o preven MAV nodes from being suck and enable hem o back off from corners and crevices and seek ou openings. This is especially useful when locaion esimaes are inaccurae. The planner employs a random exponenial back-off sraegy, where nodes move in randomly chosen direcion (uniformly from a discree number of direcions) for a ime duraion ha increases exponenially wih he number of recen collisions. This is implemened by keeping a couner for collisions in a cerain ime-window. The couner is decremened wih ime if no new collisions are encounered. 4. EVALUATION In his secion, we evaluae he performance of our sysem in planning MAVs pahs hrough physical feaure based simulaion and real experimens on a MAV esbed. Boh simulaion and real experimens are conduced in a building wih Figure 5: The figure shows he average and sandard deviaion of locaion esimaion errors a differen flying duraion heading for he near desinaion using DrunkWalk and DRMB from 5 experimens. Drunkwalk achieves around 2m locaion esimaion errors on average and 1-1.5m sandard deviaion. muliple rooms conneced wih a hallway as shown in Figure 4. The MAVs sar from he enrance and are navigaed o differen goal areas (rooms). The evaluaion focuses on he following aspecs: Characerizing he performance of he sysem in erms of 1) navigaion duraion and 2) average accuracy of locaion esimaions in comparison o exising navigaion approach. Tesing he robusness of he sysem wih changing parameers, such as number of saionary MAV nodes, noise of sensors, and radio fingerprin accuracy. Validaing he assumpions of he simulaion experimens hrough real MAV esbed experimens. For boh esbed experimens and simulaion, we compare our DrunkWalk algorihm o anoher online navigaion sraegy ha does no require any locaion infrasrucure. We briefly describe i below: Dead-Reckoning wih Map Bias (DRMB): Deadreckoning wih Map Bias is an infrasrucure-free echnique used o esimae a node s locaion in unknown environmens [12]. This mehod uses measuremens from moion sensors, opical flow and gyroscope, o esimae he change in posiion of he node. Having an esimae of locaion, we hen use he map o bias he direcion of he node s movemen similar o DrunkWalk. 4.1 Tesbed Experimen Seup To validae our sysem in a realisic seing, we implemen our algorihm on a server and he SensorFly [1] [13] MAV esbed. The SensorFly plaform used in our es has an 8-bi 16Mhz AVR AMega128rfa1 micro-conroller, a 3-axis acceleromeer, a 3-axis gyroscope, a 2-axis opical flow velociy sensor, a 3-axis magneomeers, a ulrasonic aliude sensor and a XBee radio [14]. The plaform has a fligh ime of 6-10 minues. The SensorFly nodes are capable of ranslaional and roaional moion direced by on-board PID conrol algorihms uilizing feedback from he on-board sensors.

8 Figure 6: The figure shows he cumulaive disribuion funcion (CDF) of locaion esimaion errors o arrive a near desinaion using boh DrunkWalk and DRMB from a ypical run. In our seup, we manually fly 8 MAVs on a 4m 28m arena shown in Figure 4. Six nodes are allowed o disperse and deploy as beacons a iniializaion, while 2 nodes fly o seek ou he desinaions. The nodes are inroduced o he rooms a he enrance and navigaed o 3 kinds of goal desinaions: near desinaion (room 2), medium desinaion (righ door of room 4) and far desinaion (room 5). In addiion, a laser range finder is used o rack he locaion of he nodes as ground ruh. Figure 7: The figure shows he locaion esimaion error over ime using DrunkWalk and DRMB o he medium desinaions. Mobile nodes wih DrunkWalk arrive a he desinaion earlier han hose wih DRMB due o heir capabiliy o limi he locaion esimaion errors. 4.2 Tesbed Experimen Resuls We uilize he MAV esbed o illusrae he locaion esimaion errors from shor o long disances o compare performances and robusness of DrunkWalk wih ha of DRMB. Figure 5 compares he performance and robusness of Drunk- Walk and DRMB a differen phases of navigaion duraion. We plo he average and sandard deviaion of locaion esimaion errors from 5 experimens a differen % of navigaion duraion. I is noed ha we sop he experimens a 600 seconds even if he drones do no arrive a he desinaion since his is he ypical flying ime of SensorFly node. A he firs 20% of he navigaion duraion, Drunk- Walk performs similarly as DRMB due o lack of snapsho poins o correc locaion esimaion errors. Afer his iniial period, DrunkWalk s snapsho poin correcion mainained locaion esimaion errors wihin he range of 1.5m o 2m. In conras, he error of DRMB kep accumulaing o larger han 3m. This is because muliple measuremens a snapsho poins can correc he locaion esimaion errors in DrunkWalk. In addiion, afer 30% of he navigaion ime, he sandard deviaion of DrunkWalk locaion esimaion is also 30% 60% smaller han DRMB approach. This shows DrunkWalk is more reliable han DRMB. Figure 6 shows cumulaive disribuion funcion (CDF) of locaion esimaion errors using DrunkWalk and DRMB from a ypical experimen. In DrunkWalk, correcions from snapsho poins help keep errors wihin 2.5 meers. In comparison, locaion esimaion error of DRMB remains unbounded. More han 50% of he ime, DRMB has more han 3 meers error, compared o less han 1 meer error for DrunkWalk. To illusrae he performance of DrunkWalk and DRMB for medium and far desinaions, we use Figures 7 and 8 o show single run experimen resuls. We furher evaluae hem hrough simulaed resuls in secion 4.3. Noe ha Figure 8: The figure shows he locaion esimaion error over ime using DrunkWalk and DRMB o he far desinaions. I is noed ha we do no plo all he daa for mobile node 1 since i fails o arrive a he desinaion before he baery was exhaused (600 seconds). besides he node using DRMB in he upper plo in Figure 8, he lines end when nodes reach heir desinaion. The mobile node 1 failed o arrive a he far desinaion before 600 seconds when he baery was exhaused. For boh medium and far desinaions, in he firs 20 seconds, similar o navigaion o near desinaion, DrunkWalk has similar locaion esimaion errors wih DRMB. Afer his iniial period, adequae snapsho poins help Drunk- Walk o limi he locaion esimaion errors while he error of DRMB keeps accumulaing. This shows ha muliple measuremens a snapsho poins in DrunkWalk do help limi locaion esimaion errors. The higher locaion esimaion accuracy from DrunkWalk leads o shorer (around 50%) navigaion duraion. I should be also noed ha when using DRMB, mobile node 1 fails o arrive a he far desinaion before he baery died (600 seconds) while mobile node 2 arrives a he desinaion in around 170 seconds. This shows he unreliabiliy of DRMB. On he oher hand, boh mobile node 1 and 2 wih DrunkWalk arrive a he medium and far desinaion wihin similar duraions. This shows he sabiliy of DrunkWalk wih he help of snapsho poins.

9 4.3 Physical Feaure Based Simulaion Environmen We implemened a MAV simulaion environmen [15] for he SensorFly MAV indoor sensor swarm o evaluae our planning algorihms a large scale. The simulaor includes a realisic physical arena, as well as sensor noise models, MAV mobiliy models and indoor radio signaure colleced from he esbed described earlier. For our evaluaions, we configure he simulaor as follows: Arena We use a muli-room indoor scenario shown in Figure 4, where nodes are required o auonomously navigae o differen goal areas. We collec he radio fingerprin from he real arena and feed hem ino he simulaion plaform o evaluae our sysem. This represens a ypical indoor aparmen scenario where such sysems may be deployed in search and rescue applicaions. For more complex maps, we concaenae on porions of he map in figure 4. Node Sensors The sensor nodes in he simulaion are modeled afer he SensorFly [1] MAV plaform, which is also used in our esbed experimens described in secion 4.1. Each node has a XBee radio and Dead- Reckoning sensors a gyroscope, an opical flow velociy sensor and an ulrasonic aliude measuremen sensor. Noise models are obained hrough empirical measuremens on he esbed MAV plaform. Node Mobiliy The MAV nodes can urn by a commanded angle and move for a commanded ime and velociy. We se he velociy o 1.0 m/s in accordance wih he esbed MAV parameers. The velociy of course varies in accordance wih he noisiness of he opical flow sensor, ha provides feedback o each MAV s conrol algorihm. Simulaion Time-seps The simulaion ime-sep is chosen as 1sec ha enables nodes o cover a disance of 0.8m o 1.2m in one simulaion ick. Radio The simulaion suppors esimaing received signal srengh (RSS) measuremens beween wo nodes. The RSS is colleced in he real scenario. Desinaion We adop he far desinaion (room 6) as he desinaion for simulaion since his is he hardes siuaion which shows he baseline of he sysem performance and robusness. All experimens were performed 25 imes wih 10 MAVs (6 saionary nodes and 4 mobile nodes) o evaluae boh he performance and robusness of he sysem. We run he simulaion for a ime period of 600 seconds ( 10 minues) corresponding o he ypical baery life of curren generaion MAV nodes. 4.4 Sysem Performance This secion evaluaes our sysem performance under differen desinaion consrains and ime limiaions. A successful navigaion is achieved when he node can be navigaed o he desinaion wihin he given accuracy and ime limiaion. For example, if he desinaion coordinae is (4 meers, 5 meers), he required accuracy is 1 meer and ime limi is 90 seconds, a successful navigaion means ha he mobile node can arrive wihin he range of 1 meer from (4 meers, 5 meers) wihin 90 seconds. Figure 9: The figure shows he navigaion success rae under differen desinaion accuracy consrains wihin 90 seconds for DrunkWalk and DRMB. Figure 10: The figure shows he success rae as a funcion of ime limiaion under 0.5m desinaion accuracy consrain, using DrunkWalk and DRMB alone. Figure 9 shows he navigaion success rae as a funcion of desinaion accuracy consrains wihin 90 seconds using DrunkWalk and DRMB. When he desinaion accuracy is sric (0.5 meer), DrunkWalk achieves accepable success rae of around 40% while DRMB shows less han 5%. This means ha, under very sric desinaion accuracy consrain, DRMB canno achieve he accuracy wihin he ime limiaion. while DrunkWalk can sill work wih he help of snapsho poins. For less consrained desinaion accuracy (1 meer o 2 meers), DrunkWalk shows consisenly 30% o 40% higher success rae han DRMB. Fuhermore, Drunk- Walk achieves 100% success rae for even looser desinaion accuracy consrain (2.5m) while DRMB can also ge 84% success rae. This is expeced since above 2.5 meer range is more han one half of he hallway widh (4.0 meers), where even wih high locaion esimaion errors, he mobile node can sill arrive a he desinaions simply by following he walls. Figure 10 plos he success rae as a funcion of ime limiaion for boh DrunkWalk and DRMB under a 0.5m desinaion accuracy consrain. Under a sric ime limiaion consrain (60 seconds), even DrunkWalk only achieved 8% success rae since i is no able o ge enough snapsho poins o ge accurae locaion esimaion on he way o he desinaion. When he ime limiaions are released (120 seconds o 300 seconds), DrunkWalk shows 30% o 50% higher success rae han DRMB. This is because DrunkWalk has enough ime o ge snapsho poins o correc he locaion

10 Figure 11: The figure shows he locaion esimaion error wih varying number of saionary MAV nodes using DrunkWalk and DRMB. DrunkWalk has an obvious decreasing rend when he number of saionary MAV nodes increases. I is noed ha DRMB does no use saionary MAV and is performance variance in he figure is due o noise from sensors. Figure 12: The figure shows locaion esimaion error as a funcion of opical flow noise using DrunkWalk esimaion and DRMB alone. The noise per sensor is modeled as a normal disribuion wih varying sandard deviaion. The plo shows ha DrunkWalk is able o correc he DRMB error and mainain low sandard deviaion. esimaion errors, while he error of DRMB keeps accumulaing. Afer 300 seconds, DrunkWalk achieves 100% success rae, while he success rae of DRMB becomes sable ye sill below 80%. This means ha even wih loose ime consrains, DrunkWalk sill ges more han 20% higher success rae han DRMB. 4.5 Sysem Robusness In his secion, we evaluae he robusness of our sysem by examining he locaion esimaion errors under differen sysem seups of boh DrunkWalk and DRMB Number of Saionary MAV Nodes Figure 11 shows he locaion esimaion errors for differen numbers of saionary MAV nodes, where Drunkwalk achieves 1.5 o 6 reducion for average and 1.5 o 4 reducion for sandard deviaion compared o DRMB. This shows is beer capabiliy and reliabiliy o limi locaion esimaion error. This can be aribued o improvemen on maching snapsho wih larger number of saionary nodes broadcasing beacons. We can also see he decreasing rend for boh average and sandard deviaion in Drunkwalk when he number of saionary nodes increase, which means ha increasing he number of saionary nodes do help enhance performance Navigaional Sensor Noise The noise in moion measuremens due o Dead-Reckoning sensors is an imporan parameer in deermining he evenual performance of he algorihm. Differen MAV plaforms and operaing environmens migh have differen amoun of noise in heir moion measuremens, making i useful o analyze he performance of he algorihm for varying levels of sensor noise. For our simulaions, in agreemen wih empirical measuremens on our MAV plaform, we model noise as a normal disribuion wih a sandard deviaion proporional o he sensor measuremen [7], [11]. For he opical flow velociy sensor, a noise corresponding o a normal disribuion wih 0 mean and sandard deviaion of 20% of he measured velociy value was added. For he magneomeer, Figure 13: The figure shows locaion esimaion error as a funcion of magneomeer noise using DrunkWalk esimaion and dead reckoning alone. The noise per sensor is modeled as a normal disribuion wih varying sandard deviaion. The plo shows ha DrunkWalk is able o correc he DRMB error and mainain low sandard deviaion. a 30 noise corresponds o a normal disribuion wih 0 mean and sandard deviaion of 30. The resulan noise in DRMB locaion can be compued as per he moion updae equaion [7], [11]. We apply sensor noise o boh DRMB and DrunkWalk esimaes. Figure 12 and 13 show he locaion esimaion error in DRMB and DrunkWalk for 10 nodes a various sensor noise levels. In Figure 12, wih opical flow noise level increasing from 0 o 50%, he average locaion esimaion error of DrunkWalk increases from 2.5m - 5.5m while ha of DRMB goes up very quickly o around 25 meers. The error increase is limied due o he correcions from he muliple measuremens a he same snapsho poins. In Figure 13, a faser increasing rend (from 0.5 o 7.5 meers) is observed wih he magneomeer noise increase. In addiion, similar increasing rends are observed for boh DrunkWalk and DRMB. This indicaes ha high noise from magneomeer weakens he correcion capabiliy on locaion esimaion errors. However, during

11 9, and T sig in secion Jus as rilaeraion [16], we need a leas 3 saionary nodes o esimae x and y locaion. However, due o he noise from radios, we need more saionary beacons. In our experimens, we found 6 seems o give good resuls. In order o une K and δ in Equaion 9 and he hreshold T sig for maching signaures, we refer o our previous work [7]. Afer we decide he value of K, we should se up he sample rae for snapsho poins higher han K/2 per sample according o he Nyquis-Shannon sampling heorem [17] o ensure recover he radio map. Figure 14: The figure shows locaion esimaion error as a funcion of signaure maching area for DrunkWalk and DRMB. To be noiced, DRMB does no work wih saionary MAV and noise from sensors cause he performance variance. operaion, raw magneomeer noise can be miigaed by gyroscope daa Radio Fingerprin Accuracy Locaion esimaion error depends on he resoluion o idenify snapsho on he node pahs. This is accomplished by using radio signaure from saionary MAV nodes deployed a he beginning. When a radio signaure colleced by a node a a cerain locaion is similar o a fingerprin in he daabase, he sysem classifies i as snapsho and performs he correcion of locaion esimaes. Thus, he performance of DrunkWalk depends on he resoluion of he fingerprins maching, i.e., he area or disance wihin which wo radio fingerprins can be reliably classified as being a he same locaion. If he crieria is oo loose, incorrec poins may be mached ogeher, which leads o few snapsho poins. Figure 14 shows locaion esimaion error as a funcion of signaure maching area for DrunkWalk and DRMB for 10 nodes. We observe ha DrunkWalk offers an improvemen of over 3 compared o DRMB even for a poor maching resoluion of 6m 2. In case of MAV navigaion, where he low-cos of nodes makes i possible o deploy a relaively large number of beacon nodes and aain high fingerprin accuracies of around 1m 2, DrunkWalk provides a much larger reducion in error. 5. DISCUSSION Several aspecs of DrunkWalk planning algorihm warran furher discussion and could probably lead o exensions o DrunkWalk. 5.1 Parameer Tuning We now describe how some key parameers affec he sysem performance and give some guidance on uning hem. We model all he sensor and noise disribuions according o real ess eiher by ourselves or from relaed work [7], [11]. Afer we go hese values, we use hem in our simulaion plaform and he real sysem. The signaure maching resoluion is affeced by four parameers: number of saionary nodes, K and δ in Equaion Anoher parameer, T H in secion affecs he adapive planning sraegy. The range of enropy is from 0 o log(n), where N is he number of paricles. How we se T H depends on how we hope o bias our planning sraegy. If we se T H close o 0, ha means we bias more o random walk. If we se he T H close o log(n), ha means we prefer o rusing he locaion esimaion more and bias more o follow he coarse map. Moreover, he reader can refer o [18] for guidance o se up he number of paricles. In our sysem, we adop 100 paricles for boh moion racking and snapsho poins. 5.2 Differen Layou Geomery DrunkWalk can deal wih more complicaed layou geomery and should achieve similar performance, alhough i is only esed and simulaed in a layou shown in Figure 4. The muliple rooms conneced wih a hallway in Figure 4 can be decomposed ino basic uni for complicaed layou geomery. For a differen layou geomery, we can regard i as a concaenaion of hese basic unis and se up a series of inermediae desinaions o help he drones arrive a he final desinaions. E.g. for hose muliple inerconneced rooms wih no hall layou, i is similar o he siuaion wih only room 1, room 2 and he hallway in Figure 4. In his case, we regard he hallway as a loose room inerconneced wih room 1 and room 2. In addiion, by sensing he sudden change in aliude and using a floor aliude look-up able, DrunkWalk could also deal wih muliple floor condiions. 5.3 Message Overhead In our sysem, message overhead is composed of hree pars: 1) Saionary drones broadcasing messages o flying drones for RSSI measuremens akes 1 byes for each message. Each saionary drones broadcas messages 10 imes per second. 2) Flying drones repor he RSSI values, heading informaion and some oher saus informaion o he server every second. The corresponding message size is 20 byes for each flying drone. 3) The link from server sending differen command messages o differen flying drones every second. The overhead of he command message akes 14 byes. In real sysems, due o he collision, he real overhead is ofen higher han he above value. 6. RELATED WORK Works relaed o DrunkWalk maily fall ino hree domains: sensor neworks, roboics and mobile compuing. The sensor nework domain has a number of works on deploying and navigaing mobile sensors [19, 20, 21, 22]. Howard e al. [23, 24] presen echniques for mobile sensor nework

12 deploymen in an unknown environmen. Their approach consrucs fields such ha each node is repelled by boh obsacles and by oher nodes, enabling he nework o spread iself hroughou he environmen. Similarly, Baalin e al. [25] presen a deploymen algorihm for robo eams wihou access o maps or locaion. The robos are assumed o be equipped wih vision sensors and range finders and selec a direcion away from all heir immediae sensed neighbors and move in ha direcion. The algorihm does no require communicaion beween nodes bu also does no allow nodes o be deployed a designaed locaions. The domain expers have no conrol over he emergen deploymen locaions of he nodes. The problem addressed in his paper can also be seen as an insance of he Simulaneous Localizaion And Mapping (SLAM) problem ha has been exensively sudied in he area of roboics [9, 26, 27, 28]. In fac, in he sysem we described muliple MAVs ry o localize hemselves while a he same ime rying o acquire a represenaion of he spaial disribuion of he radio signaures. In recen years here have been copious research in SLAM using eiher mehods based on Kalman filers [29, 30, 31, 32] or paricle filers [33, 34, 35, 36]. Boh approaches, however, have been mosly applied o solve insance of he SLAM problem where mobile agens are equipped wih sensors reurning disances (e.g., laser range finders, or sonars) or cameras (eiher monocular or sereo). Therefore, he ulimae objecive of hese soluions o he SLAM problem was o map physical eniies locaed in he environmen, like walls, obsacles, ec. Mehods based on Kalman filers are no applicable for he scenario we consider because we are dealing wih mulimodal, nonparameric probabiliy disribuions. Therefore, we op for a soluion based on paricle filers. Approaches based on explici percepion and processing of radio signals have been mosly aimed a implemening localizaion sysems wih he underlying assumpion ha radio signals were preliminarily colleced off line o build so-called map signals [37, 38, 39, 40]. A recen paper by Twigg e al. [41] discusses a sysem where a robo auonomously discovers he area wihin which conneciviy wih an assigned WiFi base saion is ensured. Their soluion, however, solves only he mapping side of he problem because he robo is equipped wih a laser range finder solving he localizaion problem. In oher words, RSS readings are mapped o he physical space exploiing he availabiliy of a differen sensor providing reliable localizaion. For people carrying mobile devices, SLAM-like approaches have recenly been proposed ha fuse WiFi-based RSS and moion sensor daa o simulaneously build a sensor map of he environmen and locae he user wihin his map. e.g. radio fingerprin maps [42, 43, 44, 45], or organic landmark maps [46, 47]. These approaches focus on he locaion esimaion par of an orhogonal problem, where he moion of users canno be conrolled and hence, does no involve moion planning or deploymen. Purohi e al. [7] presen a sysem for infrasrucure-free single room sweep coverage wih MAV sensor swarms. Their approach, however, does no involve he concep of locaion esimaion and navigaion and does no suppor navigaing nodes o pre-assigned desinaions. To he bes of our knowledge, his paper presens he firs aemp o solve a SLAM problem using a swarm of MAVs ha combines locaion esimaion and adapively planning o improve he success rae and accuracy of navigaion. 7. CONCLUSION This paper presens a sysem for collaboraive and adapive planning of resource-consrained MAV sensing swarms o quickly and efficienly navigae o preassigned locaions. The sysem uses collaboraion beween nodes of he swarm o overcome he sensing and compuaional limiaions of MAV nodes, and he challenging operaing environmens. We comprehensively evaluae he sysem hrough large-scale simulaions and real MAV esbed experimens showing ha DrunkWalk achieves up o 6 reducion in locaion esimaion errors, and as much as 3 improvemen in navigaion success rae under he given ime and accuracy consrains. 8. ACKNOWLEDGEMENTS We would like o hank our shepherd Prof. Akos Ledeczi and he anonymous reviewers for heir insighful and consrucive commens. This research was suppored by Inel, Nokia, NSF under he gran CNS and CNS , and DARPA under he gran D11AP The 4h auhor Sefano Carpin is parially suppored by he Army Research Lab under conrac MAST-CNC Any opinions, findings, and conclusions or recommendaions expressed in hese maerials are hose of he auhor and should no be inerpreed as represening he official policies, eiher expressly or implied, of he funding agencies of he U.S. Governmen. 9. REFERENCES [1] A Purohi, Zheng Sun, F Mokaya, and Pei Zhang. SensorFly: Conrolled-mobile sensing plaform for indoor emergency response applicaions. In Proceeding of he 10h Inernaional Conference on Informaion Processing in Sensor Neworks (IPSN), pages , [2] Rober J. Wood. The Firs Takeoff of a Biologically Inspired A-Scale Roboic Insec. IEEE ransacions on roboics, 24(2): , [3] Karhik Danu, Bryan Kae, Jason Waerman, Peer Bailis, and Ma Welsh. Programming micro-aerial vehicle swarms wih karma. In Proceedings of he 9h ACM Conference on Embedded Neworked Sensor Sysems, SenSys 11, pages , New York, NY, USA, ACM. [4] Mahew Turpin, Nahan Michael, and Vijay Kumar. Trajecory design and conrol for aggressive formaion fligh wih quadroors. Auonomous Robos, 33(1-2): , February [5] S. Shen, N. Michael, and V. Kumar. Vision-based auonomous navigaion in complex environmens wih a quadroor. In iros, Tokyo, Japan, nov [6] Ryan Morlok and Maria Gini. Dispersing robos in an unknown environmen. In 7h Inernaional Symposium on Disribued Auonomous Roboic Sysems (DARS ), [7] Aveek Purohi, Zheng Sun, and Pei Zhang. Sugarmap: Locaion-less coverage for micro-aerial sensing swarms. In Proceedings of he 12h Inernaional Conference on